I need only short answer a, b, c, d

1. A company has 4 machines that will fail randomly every time. On average each machine will fail twice a day. The machines are repaired by a mechanic by spending an average of 3 hours on each machine. Determine the traffic intensity or utilization factor: a. 1/6 b. 2 c. 1/3 d. 2/3 2. The following is a false statement; a. The irreducible Markov chain has no communicating states b. The state class is a set of states that communicate with each other c. not all states are transient states d. A state that is not in the same state class is a state that does not communicate with each other 3. Determine the false statement of the transition matrix P above: a. there are two state classes b. there is 1 state class c. state 2 and state 4 communicate with each other d. statel and state 5 communicate with each other 4. Determine which model is appropriate for a system with a fixed service time (constant), 1 server and the arrival of events is a poison process: a. M/M/l b. MID/1 c. DIM/1 cl. DID/1 5. The following distributions are classified as examples of discrete random variables, except: a. normal b. Bernouli c. Geometry d. Poisson 6. The following are the correct terms used in determining stationary probability in queuing theory: a. Is = number of expected average units in the queue b. W5 = Expected average waiting time in the system c. I = number of expected average units in the system d. P0 = probability that there are customers in the system 7. All of the following are true regarding the stationary probability of continuous-time Markov chain, Except a. state iexit rate = statej . exit rate b. sum of all stationary probabilities = 1 c. The process of birth and death is a continuous time Markov chain cl. when the system is in state 0 (there are no individuals in the system), then only processes may transition to statel The following statements are false, except a. state 1 and state 2 are not in the same state class b. Markov chain reaches stationary probability [there is a 6th step c. the probability that the stationary process is in state 1 is 0.926316 9. If 0 ={1,2,3,4,5,6] is the sample space of throwing one dice. Here are the subsets of Q : a. 1 b. {2,4,5} c. {va29de Z +} d. 2 I10. All of the following are true statements regarding the Poisson process and the intermingling process (m process), except: a. The poison process is stated that the time between arrivals is a random variable that is independent of each other and has an identical Poisson distribution b. With probability 1, then: ma lfor taco '7 M c. The renewal process is a stochastic process in which the time between arrivals and events is a random variable that is independent of each other and has an arbitrary distribution. d. The renewel process is the process of counting the number of independent events